Liu hard disk equation of state - Revision history

QH97: The definition of alpha was missing a -1. See right below Equation (13) on pp. 5 of Liu's paper.

2024-02-28T17:53:46Z

The definition of alpha was missing a -1. See right below Equation (13) on pp. 5 of Liu's paper.

← Older revision		Revision as of 19:53, 28 February 2024
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	<math>Z_{solid} = \frac{2}{\alpha} + 1.9 + \alpha - 5.2 \alpha^2 + 114.48 \alpha^4</math>		<math>Z_{solid} = \frac{2}{\alpha} + 1.9 + \alpha - 5.2 \alpha^2 + 114.48 \alpha^4</math>

	and <math>\alpha = \frac{2}{3^{1/2} \rho \sigma^2}</math>		and <math>\alpha = \frac{2}{3^{1/2} \rho \sigma^2} - 1</math>

2020-11-11T01:59:11Z

← Older revision		Revision as of 03:59, 11 November 2020
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	For the stable fluid:		For the stable fluid:
	:<math>Z_v = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math>		:<math>Z_v = \frac{1 + \eta^2/8 + \eta^3/18 - 4 \eta^4/21}{(1-\eta)^2} </math>

	where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where <math>\rho</math> is density and <math>\sigma</math> is the diameter of the disks.		where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where <math>\rho</math> is density and <math>\sigma</math> is the diameter of the disks.

2020-10-27T09:51:23Z

Expanded the reference details

← Older revision		Revision as of 11:51, 27 October 2020
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	The '''Liu''' [[Equations of state \| equation of state]] for [[hard disks]] (2-dimensional [[hard sphere model \| hard spheres]]) is given by Eq. 1, 9 and 13 of		The '''Liu''' [[Equations of state \| equation of state]] for [[hard disks]] (2-dimensional [[hard sphere model \| hard spheres]]) is given by Eq. 1, 9 and 13 of
	<ref>[https://arxiv.org/abs/2010.10624]</ref>.		<ref>[https://arxiv.org/abs/2010.10624 Hongqin Liu "Global equation of state and phase transitions of the hard disc systems", arXiv:2010.10624 (2020)]</ref>.

	For the stable fluid:		For the stable fluid:

2020-10-24T18:59:35Z

← Older revision		Revision as of 20:59, 24 October 2020
Line 5:		Line 5:
	:<math>Z_v = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math>		:<math>Z_v = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math>

	where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where <math>\sigma</math> is the diameter of the disks.		where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where <math>\rho</math> is density and <math>\sigma</math> is the diameter of the disks.

	The EoS for the stable fluid, liquid-hexatic transition region and hexatic:		The EoS for the stable fluid, liquid-hexatic transition region and hexatic:

2020-10-24T14:41:34Z

2020-10-24T14:40:50Z

2020-10-22T19:13:10Z

← Older revision		Revision as of 21:13, 22 October 2020
Line 1:		Line 1:
	The '''Liu''' [[Equations of state \| equation of state]] for [[hard disks]] (2-dimensional [[hard sphere model \| hard spheres]]) is given by Eq. 1 of		The '''Liu''' [[Equations of state \| equation of state]] for [[hard disks]] (2-dimensional [[hard sphere model \| hard spheres]]) is given by Eq. 1, 9 and 13 of
	<ref>[https://arxiv.org/abs/2010.10624]</ref>.		<ref>[https://arxiv.org/abs/2010.10624]</ref>.

2020-10-22T19:11:18Z

2020-10-22T19:10:47Z

2020-10-22T19:09:28Z

@@ Line 19: / Line 19: @@
 <math>Z_{solid} = \frac{2}{\alpha} + 1.9 + \alpha - 5.2 \alpha^2 + 114.48 \alpha^4</math>
-where <math>\alpha = \frac{2}{3^{1/2} \rho \sigma^2}</math>
+and <math>\alpha = \frac{2}{3^{1/2} \rho \sigma^2}</math>
 ==References==